The law allows authorities to bar foreign civil society groups seen as threatening Russia's "defence capabilities" or "consitutional foundations" and go after local activists working with them, the Kremlin statement said.
Supporters presented the law as a "preventative measure", necessary after the wave of Western sanctions put in place over the Ukraine conflict.
Under the law, passed by the Russian parliament this week, authorities can ban foreign NGOs and go after their employees, who risk up to six years in prison or being barred from the country.
Lawmakers cited the need to stop "destructive organisations" working in Russia, which could threaten the "value of the Russian state" and stir up "colour revolutions", the name given to pro-Western movements seen in some former Soviet republics over the last several years.
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Critics have said that the vague wording of the law -- which gives Russia's general prosecutor the right to impose the "undesirable" tag without going to court -- could allow officials to target foreign businesses working in Russia.
The measure complements legislation already passed in 2012, which forces NGOs that receive foreign funds to register as a "foreign agent.